Finite Group Databasebeta

← #34060743

Subgroups — #34060743

Order 19072.

308 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750703C211yesmaximal, characteristic
2#23750612C211yesmaximal, characteristic
3C2×#18011972C212yesmaximal, complemented
4#23750506C212yesmaximal, complemented
5#23750197C211yesmaximal, characteristic
6#18011998—24no—
7D149⋊M16—21no—
8C2×#14558745—21no—
9C2×#14558745C2212yes—
10C2×#14558745C2212yes—
11#18011972—24no—
12#18011972—21no—
13#18011971—21no—
14C2×#14558735C2211yescharacteristic
15C22×Dic298C2211yescharacteristic
16#18011910—21no—
17#18011897—21no—
18#18011895C411yescharacteristic
19#18011894C411yescharacteristic
20#18011892C411yescharacteristic
21#18011889—21no—
22#18011888—21no—
23#18011867C2211yescharacteristic
24#123×C149C411yescharacteristic
25#14558746—22no—
26#14558745—22no—
27#14558745—22no—
28#14558745—22no—
29#14558745—22no—
30#14558745D414yes—
31D149⋊C8—22no—
32C2×#11924753—22no—
33C2×#11924753—22no—
34C2×#11924753—22no—
35#14558735—22no—
36#14558735—22no—
37C2×Dic298—21no—
38C2×Dic298—22no—
39C2×Dic298—21no—
40C2×Dic298—22no—
41C2×Dic298D411yescharacteristic
42C2×C22⋊D149C2×C411yescharacteristic
43C2×C22⋊D149D411yescharacteristic
44C22×Dic149C2×C411yescharacteristic
45C22×Dic149D411yescharacteristic
46C22×Dic149C2311yescharacteristic
47C2×C4×D149D411yescharacteristic
48C4⋊Dic149—21no—
49#14558715—21no—
50#14558715—21no—
51#14558715—21no—
52C22⋊Dic149—21no—
53C22⋊Dic149C2×C411yescharacteristic
54#14558713—21no—
55#14558713—21no—
56C4×Dic149—21no—
57C2×D4×C149C2×C411yescharacteristic
58C22×C4×C149C2×C411yescharacteristic
59C4⋊C4×C149—21no—
60C22⋊C4×C149—21no—
61C22⋊C4×C149C2×C411yescharacteristic
62#11924753—24no—
63#11924753—42no—
64C22×D149C22⋊C411yescharacteristic
65Dic298—22no—
66Dic298—41no—
67Dic298—42no—
68Dic298—41no—
69C22⋊D149—22no—
70C22⋊D149—22no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—21no—
74C2×Dic149—21no—
75C2×Dic149—22no—
76C2×Dic149C22⋊C411yescharacteristic
77C2×Dic149C2×D412yes—
78C2×Dic149C2×D411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C2×Dic149#4112yes—
81C4×D149—21no—
82C4×D149—21no—
83C23×C149C22⋊C411yescharacteristic
84C23×C149C22×C411yescharacteristic
85D4×C149—22no—
86C2×C4×C149—21no—
87C2×C4×C149—21no—
88C2×C4×C149—22no—
89C2×C4×C149C22⋊C411yescharacteristic
90C22×C149—21no—
91C22×C149—41no—
92C22×C149—41no—
93C22×C149C2×C22⋊C411yescharacteristic
94C22×C149C4×D412yes—
95C2×D149—21no—
96C2×D149—41no—
97C4×C149—21no—
98C4×C149—41no—
99C4×C149—41no—
100Dic149—21no—
101Dic149—41no—
102Dic149—41no—
103Dic149#12011yescharacteristic
104Dic149#12112yes—
105Dic149#12311yescharacteristic
106C2×C149—21no—
107C2×C149—22no—
108C2×C149—41no—
109C2×C149#38611yescharacteristic
110D149—41no—
111C149#191511yescharacteristic, complemented, Sylow
112#1915—1491nomaximal, Sylow
113#568—1491no—
114#536—1491no—
115#413—1491no—
116C2×#101—1492no—
117#344—1492no—
118C2×#41—1491no—
119C22×Q8—1491no—
120#131—2984no—
121C2×M16—2981no—
122C2×M16—2981no—
123C2×M16—1492no—
124C2×M16—1492no—
125C4⋊Q8—2981no—
126#124—2981no—
127#123—1491no—
128#123—1491no—
129#123—1491no—
130#123#1059701011yescharacteristic
131C22⋊Q8—2981no—
132C22⋊Q8—2981no—
133#117—1491no—
134#101—2981no—
135#101—2984no—
136#100—2981no—
137#41—2982no—
138#41—2982no—
139C2×Q8—2982no—
140C2×Q8—2981no—
141C2×Q8—2981no—
142C2×Q8—2982no—
143C2×Q8—1491no—
144C2×D4—1491no—
145C2×D4—1491no—
146C2×D4C2×#1059701011yescharacteristic
147C22×C4—1491no—
148C22×C4—1491no—
149C22×C4—1491no—
150C22×C4—1491no—
151C22×C4C2×#1059701011yescharacteristic
152M16—2982no—
153M16—2982no—
154M16—2982no—
155M16—2982no—
156M16—2982no—
157M16—1494no—
158C2×C8—2982no—
159C2×C8—2982no—
160C2×C8—2982no—
161C2×C8—2982no—
162C4⋊C4—21no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—2981no—
166C4⋊C4—2981no—
167C22⋊C4—21no—
168C22⋊C4—2981no—
169C22⋊C4—2981no—
170C22⋊C4—2981no—
171C22⋊C4—1491no—
172C22⋊C4C2×#1059701011yescharacteristic
173C42—2981no—
174C23—1491no—
175C23C22⋊#1059701011yescharacteristic
176C23C22×#1059701011yescharacteristic
177Q8—2982no—
178Q8—5961no—
179Q8—5962no—
180Q8—5961no—
181D4—22no—
182D4—2982no—
183D4—2982no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—2981no—
188C2×C4—2981no—
189C2×C4—2981no—
190C2×C4—2981no—
191C2×C4—2981no—
192C2×C4—2981no—
193C2×C4—2982no—
194C2×C4—1491no—
195C2×C4—1491no—
196C2×C4—1491no—
197C2×C4—1492no—
198C2×C4—1492no—
199C2×C4C22⋊#1059701011yescharacteristic
200C8—2984no—
201C8—5962no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—2981no—
206C22—5961no—
207C22C2×C22⋊#1059701011yescharacteristic
208C22D4×#1059701012yes—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—2981no—
213C4—5961no—
214C4—5961no—
215C4—1491no—
216C4—1492no—
217C4—1491no—
218C2—21no—
219C2—22no—
220C2—41no—
221C2—5961no—
222C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
Fitting#123×C149C4
socleC2×C149#386
prime radicalC2×#14558735C22
cosocleC22×Dic149C23
hypercenter#123#10597010
hypocenterC149#1915
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#18011972C2semidirect
4. #23750506C2semidirect
111. C149#1915semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237507032
#237506122
C2×#180119722
#237505062
#237501972
#1915149